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TWO ALGORITHMS FOR LC^1 UNCONSTRAINED OPTIMIZATION

Journal of Computational mathematics 2000年第6期18卷 621-632页

作者： Wen-yu Sun R.J.B.de Sampaio Jin-Yun Yuan School of Mathematics and Computer Science Nanjing Normal UniversityNanjing 210097China Applied Informatics Program Pontifical Catholic University of ParanaCuritibaPR81611-970Brazil Department of Mathematics Federal University of ParanaCuritibaPR81531-990Brazil

Presents two algorithms for LC unconstrained optimization problems which use the second order Dini upper directional derivative. Simplicity of the methods to use and perform; Discussion of related properties of the it... 详细信息

关键词： nonsmooth optimization directional derivative Newton-like method convergence trust region method

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Conservative Semi-Lagrangian Finite Difference WENO Formulations with Applications to the Vlasov Equation

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Communications in Computational Physics 2011年第9期10卷 979-1000页

作者： Jing-Mei Qiu Chi-Wang Shu Department of Mathematical and Computer Science Colorado School of MinesGoldenCO 80401USA Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA

In this paper,we propose a new conservative semi-Lagrangian(SL)finite difference(FD)WENO scheme for linear advection equations,which can serve as a base scheme for the Vlasov equation by Strang splitting[4].The reconstruction procedure in the proposed SL FD scheme is the same as the one used in the SL finite volume(FV)WENO scheme[3].However,instead of inputting cell averages and approximate the integral form of the equation in a FV scheme,we input point values and approximate the differential form of equation in a FD spirit,yet retaining very high order(fifth order in our experiment)spatial *** advantage of using point values,rather than cell averages,is to avoid the second order spatial error,due to the shearing in velocity(v)and electrical field(E)over a cell when performing the Strang splitting to the Vlasov *** a result,the proposed scheme has very high spatial accuracy,compared with second order spatial accuracy for Strang split SL FV scheme for solving the Vlasov-Poisson(VP)*** perform numerical experiments on linear advection,rigid body rotation problem;and on the Landau damping and two-stream instabilities by solving the VP *** comparison,we also apply(1)the conservative SL FD WENO scheme,proposed in[22]for incompressible advection problem,(2)the conservative SL FD WENO scheme proposed in[21]and(3)the non-conservative version of the SL FD WENO scheme in[3]to the same test *** performances of different schemes are compared by the error table,solution resolution of sharp interface,and by tracking the conservation of physical norms,energies and entropies,which should be physically preserved.

关键词： Semi-Lagrangian methods finite difference/finite volume scheme conservative scheme WENO reconstruction Vlasov equation Landau damping two-stream instability

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MatterChat: A Multi-Modal LLM for Material science

arXiv

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arXiv 2025年

作者： Tang, Yingheng Xu, Wenbin Cao, Jie Ma, Jianzhu Gao, Weilu Farrell, Steve Erichson, Benjamin Mahoney, Michael W. Nonaka, Andy Yao, Zhi Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA United States NSF National AI Institute for Student-AI Teaming University of Colorado at Boulder Boulder United States Institute for AI Industry Research Tsinghua University Beijing China Department of Electrical and Computer Engineering The University of Utah Salt Lake CityUT United States Scientific Data Division Lawrence Berkeley National Laboratory BerkeleyCA United States International Computer Science Institute BerkeleyCA United States Department of Statistics University of California at Berkeley BerkeleyCA United States

Understanding and predicting the properties of inorganic materials is crucial for accelerating advancements in materials science and driving applications in energy, electronics, and beyond. Integrating material structure data with language-based information through multi-modal large language models (LLMs) offers great potential to support these efforts by enhancing human–AI interaction. However, a key challenge lies in integrating atomic structures at full resolution into LLMs. In this work, we introduce MatterChat, a versatile structure-aware multi-modal LLM that unifies material structural data and textual inputs into a single cohesive model. MatterChat employs a bridging module to effectively align a pretrained machine learning interatomic potential with a pretrained LLM, reducing training costs and enhancing flexibility. Our results demonstrate that MatterChat significantly improves performance in material property prediction and human-AI interaction, surpassing general-purpose LLMs such as GPT-4. We also demonstrate its usefulness in applications such as more advanced scientific reasoning and step-by-step material synthesis. © 2025, CC BY.

关键词： Materials properties

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Hierarchical clustering via localized diffusion folders

Hierarchical clustering via localized diffusion folders

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2010 AAAI Fall Symposium

作者： David, Gil Averbuch, Amir Coifman, Ronald R. Department of Mathematics Program in Applied Mathematics Yale University United States School of Computer Science Tel-Aviv University Israel

We present a short introduction to an hierarchical clustering method of high-dimensional data via localized diffusion folders. Copyright © 2010, Association for the Advancement of Artificial Intelligence. All rig... 详细信息

ISBN: (纸本)9781577354888

关键词： Clustering algorithms

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A Novel Multiple Dependent State Sampling Plan Based on Time Truncated Life Tests Using Mean Lifetime

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computers, Materials & Continua 2022年第12期73卷 4611-4626页

作者： Pramote Charongrattanasakul Wimonmas Bamrungsetthapong Poom Kumam Division of Mathematics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology KrungthepBangkok10120Thailand Division of Applied Statistics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology ThanyaburiPathum Thani12110Thailand Center of Excellence in Theoretical and Computational Science(TaCS-CoE)&KMUTT Fixed Point Research Laboratory Room SCL 802 Fixed Point LaboratoryScience Laboratory BuildingDepartments of MathematicsFaculty of ScienceKing Mongkut’s University of Technology Thonburi(KMUTT)Bangkok10140Thailand

The design of a new adaptive version of the multiple dependent state(AMDS)sampling plan is presented based on the time truncated life test under the Weibull *** achieved the proposed sampling plan by applying the concept of the double sampling plan and existing multiple dependent state sampling plans.A warning sign for acceptance number was proposed to increase the probability of current lot *** optimal plan parameters were determined simultaneously with nonlinear optimization problems under the producer’s risk and consumer’s risk.A simulation study was presented to support the proposed sampling plan.A comparison between the proposed and existing sampling plans,namely multiple dependent state(MDS)sampling plans and a modified multiple dependent state(MMDS)sampling plan,was considered under the average sampling number and operating characteristic curve *** addition,the use of two real datasets demonstrated the practicality and usefulness of the proposed sampling *** results indicated that the proposed plan is more flexible and efficient in terms of the average sample number compared to the existing MDS and MMDS sampling plans.

关键词： Adaptive version of multiple dependent state sampling plan time truncated life test quality level weibull distribution mean lifetime

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Concentration and relative entropy for compound poisson distributions

Concentration and relative entropy for compound poisson dist...

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2005 IEEE International Symposium on Information Theory, ISIT 05

作者： Madiman, M. Kontoyiannis, I. Division of Applied Mathematics Brown University Providence RI 02912 United States Division of Applied Mathematics Department of Computer Science Brown University Providence RI 02912 United States

ISBN: (纸本)0780391519

Using a simple inequality about the relative entropy, its so-called "tensorization property," we give a simple proof of a functional inequality which is satisfied by any compound Poisson distribution. This functional inequality belongs to the class of modified logarithmic Sobolev inequalities. We use it to obtain measure concentration bounds for compound Poisson distributions under a variety of assumptions on their tail behavior. In particular, we show how the celebrated "Herbst argument" can be modified to yield sub-exponential concentration bounds. For example, suppose Z is a compound Poisson random variable with values on the nonnegative integers, and let f be a function such that |f(k+1)- f(k)| &le 1 for all k. Then, if the base distribution of Z does not have a finite moment-generating function but has finite moments up to some order L > 1, we show that the probability that f(Z) exceeds its mean by a positive amount t or more decays approximately like (const)·t-L, where the constant is explicitly identified. This appears to be one of the very first examples of concentration bounds with power-law decay.

关键词： Information theory

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Characterization of VAX macsyma 81

Characterization of VAX macsyma

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4th ACM Symposium on Symbolic and Algebraic Computation, SYMSAC 1981

作者： Faderaro, Jahn K. Fateman, Richard J. Computer Science Division Center for Pure and Applied Mathematics University of California BerkeleyCA United States

ISBN: (纸本)0897910478

Vaxima spends a great, deal of time moving data from one place to another. When this data movement is done in compiled lisp, much of it is simply stacking arguments prior to calling a function. Since there are a large number of function calls, we would like to optimize the calling sequence, yet maintain compatibility with the C calling sequence. Our compromise was to code in assembler language those small functions which were called most often, enabling us to change the way those functions were called. The results given above demonstrate the efficacy of this approach and suggest that we should recade the equal function in assembler as well. The Franz Lisp compiler does not do very much to optimize the fixnum arithmetic operations. As our results indicate, it would be a waste of effort to modify the compiler to handle fimums if all we were interested in was running Vaxima on problems such as those found in the Begin demo. Only a small amount of arithmetic is done in Vaxima and most of that is written in C where it would be unaffected by a compiler change.

关键词： program compilers

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A Pseudo-Spectral Scheme for Systems of Two-Point Boundary Value Problems with Left and Right Sided Fractional Derivatives and Related Integral Equations

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computer Modeling in Engineering & sciences 2021年第7期128卷 21-41页

作者： I.G.Ameen N.A.Elkot M.A.Zaky A.S.Hendy E.H.Doha Department of Mathematics Faculty of ScienceAl-Azhar UniversityCairoEgypt Department of Mathematics Faculty of ScienceCairo UniversityGiza12613Egypt Department of Applied Mathematics Physics DivisionNational Research CentreDokkiCairo12622Egypt Department of Computational Mathematics and Computer Science Institute of Natural Sciences and MathematicsUral Federal UniversityYekaterinburg620002Russia Department of Mathematics Faculty of ScienceBenha UniversityBenha13511Egypt

We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left-and right-sided fractional *** main ingredient of the proposed method is to recast the problem into an equivalent system of weakly singular integral ***,a Legendre-based spectral collocation method is developed for solving the transformed ***,we can make good use of the advantages of the Gauss quadrature *** present the construction and analysis of the collocation *** results can be indirectly applied to solve fractional optimal control problems by considering the corresponding Euler–Lagrange *** numerical examples are given to confirm the convergence analysis and robustness of the scheme.

关键词： Spectral collocation method weakly singular integral equations two-point boundary value problems convergence analysis

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Preventing Pressure Oscillations Does Not Fix Local Linear Stability Issues of Entropy-Based Split-Form High-Order Schemes

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Communications on applied mathematics and Computation 2022年第3期4卷 880-903页

作者： Hendrik Ranocha Gregor J.Gassner Applied Mathematics Münster University of Münster48149 MünsterGermany Computer Electrical and Mathematical Science and Engineering(CEMSE)Division King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia Department of Mathematics and Computer Science Center for Data and Simulation ScienceUniversity of CologneCologneGermany

Recently,it was discovered that the entropy-conserving/dissipative high-order split-form discontinuous Galerkin discretizations have robustness issues when trying to solve the sim-ple density wave propagation example for the compressible Euler *** issue is related to missing local linear stability,i.e.,the stability of the discretization towards per-turbations added to a stable base *** is strongly related to an anti-diffusion mech-anism,that is inherent in entropy-conserving two-point fluxes,which are a key ingredi-ent for the high-order discontinuous Galerkin *** this paper,we investigate if pressure equilibrium preservation is a remedy to these recently found local linear stability issues of entropy-conservative/dissipative high-order split-form discontinuous Galerkin methods for the compressible Euler *** equilibrium preservation describes the property of a discretization to keep pressure and velocity constant for pure density wave *** present the full theoretical derivation,analysis,and show corresponding numerical results to underline our *** addition,we characterize numerical fluxes for the Euler equations that are entropy-conservative,kinetic-energy-preserving,pressure-equilibrium-preserving,and have a density flux that does not depend on the *** source code to reproduce all numerical experiments presented in this article is available online(https://***/10.5281/zenodo.4054366).

关键词： Entropy conservation Kinetic energy preservation Pressure equilibrium preservation Compressible Euler equations Local linear stability Summation-by-parts

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Stylistic analysis of paintings using wavelets and machine learning

Stylistic analysis of paintings using wavelets and machine l...

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17th European Signal Processing Conference, EUSIPCO 2009

作者： Jafarpour, Sina Polatkan, Güngör Brevdo, Eugene Hughes, Shannon Brasoveanu, Andrei Daubechies, Ingrid Princeton University Departments of Electrical Engineering Computer Science and Mathematics Program in Applied and Computational Mathematics Princeton NJ 08544 United States

Wavelet transforms and machine learning tools can be used to assist art experts in the stylistic analysis of paintings. A dual-tree complex wavelet transform, Hidden Markov Tree modeling and Random Forest classifiers are used here for a stylistic analysis of Vincent van Gogh's paintings with results on two stylometry challenges that concern "dating, resp. extracting distinguishing features". © EURASIP, 2009.

关键词： Decision trees

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